The correct tire pressure is the pressure that will result in a maxium tire contact area with the road. This pressure will wear the tires evenly and provide the safest ride with maximum traction available for braking and turning. Fuel economy and ride "feel" should not be the criteria.
That being said, the correct tire pressure for your particular vehicle will vary with ambient temperature, vehicle weight, and tire make/model.
Best way to determine if you have the correct pressure is to use a method that was recommended by a friend of mine. You'll need a piece of your child's sidewalk chalk for this test. In a parking lot with the car in its "usual" driving conditions (i.e., load, temperature, etc.), draw a chalk line across the tread of your tires. Get back in the car and roll the car 10-20 feet (enough for a few complete tire revolutions) and check the chalk marks. If the marks show even wear, then your tires are properly inflated. Simple.
If the chalk marks show more wear in the center of the tread, then your pressure is too high. If the chalk marks show wear on the outside edges of the tread, then your pressure is too low.
Remember to thank your child for lending his/her chalk.